# EVALUATE RATIONAL EXPRESSIONS

## About "Evaluate rational expressions"

Evaluate rational expressions :

Evaluating rational expression means we have to apply the given value in the given rational expression instead of the variable that we find the question.

Let us see some examples based on the above concept.

Example 1 :

Evaluate the following rational expression Solution :

=  (x² - 4)/3x

Here we need to apply the value 5 instead of the variable "x".

=  (5² - 4)/3(5)

=  (25 - 4)/15

=   21/15

Divide the numerator and the denominator by 3

=  7/5

Hence the answer is 7/5

Example 2 :

Evaluate the following rational expression Solution :

=  (m + P)/5

Here we need to apply the value 1 instead of the variable "m" and apply the value 5 instead of p.

=  (1 + 5)/5

=  6/5

Hence the answer is 6/5

Example 3 :

Evaluate the following rational expression Solution :

=  (p²m)/4

Here we need to apply the value 7 instead of the variable "p" and apply the value 4 instead of m.

=  [7²(4)]/4

=  (49 x 4)/4  =  49

Hence the answer is 49.

Example 4 :

Evaluate the following rational expression Solution :

=  (p³ + 10)/m

Here we need to apply the value 9 instead of the variable "m" and apply the value 2 instead of p.

=  (2³ + 10)/9

=  (8 + 10)/9

=  18/9  =  2

Hence the answer is 2.

Example 5 :

Evaluate the following rational expression Solution :

=  (a² - b)/6

Here we need to apply the value 5 instead of the variable "a" and apply the value 1 instead of b.

=  (5² - 1)/6

=  (25 - 1)/6

=  24/6  =  4

Hence the answer is 4.

Example 6 :

Evaluate the following rational expression Solution :

=  (y - z)/(zx - 6)

Here we need to apply the value 3 instead of the variable "x", apply the value 4 instead of "y" and apply the value 4 instead of the variable "z"

=  (4 - 4)/(4(3) - 6)

=  0/(12 - 6)

=  0/6  =  0

Hence the answer is 0.

Example 7 :

Evaluate the following rational expression

(x + 3)/(2x - 5) where x = 4

Solution :

=  (x + 3)/(2x - 5)

=  (4 + 3)/(2(4) - 5)

=  7/(8 - 5)

=  7/3

Hence the answer is 7/3.

Example 8 :

Evaluate the following rational expression

(x - 2)/(x² + 2x - 8) where x = 3

Solution :

=  (x - 2)/(x² + 2x - 8)

Here we need to apply the value "3" instead of the variable "x" in the above rational expression.

=  (3 - 2)/(3² + 2(3) - 8)

=  1/(9 + 6 - 8)

=  1/(15 - 8)

=  1/7

Hence the answer is 1/7.

After having gone through the stuff given above, we hope that the students would have understood "Evaluate rational expressions".

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